The Increment in Nuclear Binding
Energy Due to the Formation of
a Neutron-Neutron Spin Pair

The conventional theory of what holds a nucleus together is based upon the assumption that all nucleons
(neutrons and protons) attract each other equally. This attraction was given the name "nuclear strong force."
There is no more empirical content to this name than something that holds nuclei together. It superficially
explains the existence of stable nuclei, but fails to explain, among other things, why there limits to the number of
neutrons in nuclei with various numbers of protons.

The nucleons in a nucleus are held together largely by their spin pairing. See Nucleus for
the details on this. The material below provides estimates of the binding energy due the formation of neutron-neutron spin pairs
and its variation with the location within the nucleus where they are formed.

Consider first the incremental binding energies of the isotopes of Tin. Tin has the greatest number of stable isotopes
of any element. Those incremental binding energies are shown below.

The peaks represent the formation of a spin pair.
The sharp break after 82 neutrons represents the filling of a shell.
The difference in the sizes of the peaks before and after 82 neutrons shows that
the binding energy due to spin pair formations is not the same at all locations
in the nucleus however it could be roughly constant within a nuclear shell

The binding energy due to the formation of a spin pair can be
computed as the difference in the incremental binding energy at
one point and the average of the value at the two adjacent points,
as shown below.

This procedure is not valid at a point where there is a change
in shell.

This procedure applied to the incremental binding energies of the Tin
isotopes gives the following results.

The values are more or less constant within the 51-82 shell, but definitely
drop for the 83-126 shell.

In the 51-82 shell the average increment due to neutron-neutron spin pair formation is
2.63 MeV with a standard deviation of
0.161 MeV. Thus the coefficient of variation is
6.1 percent.

To see how the binding energy increments due to neutron-neutron spin pair formation
are affected by the number of protons in the nucleus the values were calculated also for p=49 and
p=51.

The Binding Energies Due to Neutron-Neutron Spin Pair Formation
for the Isotopes of Indium (p=49), Tin (p=50), Antimony (p=51).

Numberof neutrons

BEnn p=49(MeV)

BEnn p=50(MeV)

BEnn p=51 (MeV)

51

2.45

52

1.85

2.8

53

2.6555

2.675

54

2.8415

2.625

1.305

55

2.459

2.71

1.805

56

2.1155

2.795

2.13

57

2.0545

2.695

2.2

58

2.1235

2.569

2.19

59

2.143

2.6935

2.25

60

2.1345

2.83

2.289

61

2.168

2.8485

2.2985

62

2.12

2.8245

2.2965

63

2.0375

2.7995

2.301

64

1.967

2.6545

2.2835

65

1.967

2.3855

2.259

66

2.01

2.319

2.2385

67

2.1175

2.5015

2.2945

68

2.1925

2.6125

2.3245

69

2.2955

2.732

2.37495

70

2.3135

2.7789

2.3284

71

2.2535

2.7892

2.2966

72

2.213

2.7552

2.3281

73

2.2365

2.70465

2.37195

74

2.2595

2.648

2.3777

75

2.2845

2.6075

2.3462

76

2.2215

2.5475

2.299

77

2.07

2.48875

2.2655

78

1.845

2.4425

2.1825

79

1.545

2.436

2.052

80

1.43

2.405

1.8855

81

1.4

2.29

1.72

82

2.575

3.495

2.853

83

2.325

3.105

2.416

84

0.77

1.42

0.725

83

2.325

3.105

2.416

84

0.77

1.42

0.725

85

1.55

0.765

86

1.64

0.815

87

0.9

Here are the data plotted.

Clearly there is something special about the case of p=50.
Its values are higher than those for p=49 and p=51.

Lead

The binding energy due to the formation of a neutron-neutron spin pair
can only be estimated away from the filling of the neutron shell at n=126.

Gold

The Magnetic MetalsIron, Cobalt and Nick

The binding energy due to spin pair formation is roughly constant
within shells but if affected by the proton number.

Conclusions

Clearly the binding energy due to the formation of a neutron-neutron spin pair
is not independent of location. It varies within a shell as well as between shells.

The relationships are "continuous" in the sense that the changess from one step to
the next are relatively small.